Question

Determine whether the scenario below involves permutations or combinations.

At a family gathering, 32 people are trying to fit into several cars. Your car holds 6 people. How many different groups of 6 could you take in your car?

Answer 1

is this a combination question? & if so would u do 32 C 6 ?

Answer 2

do u know it?

Answer 3

http://answers.yahoo.com/question/index?qid=20111129141443AAOMYOP
whats 32 C 6?

Answer 4

that's the same as doing:
32!/ 6! (32-6)!

Answer 5

@AwesomeB

Answer 6

http://openstudy.com/study#/updates/4dca97a140ec8b0bf4d10f17

Answer 7

Check that last link, I think it will help you!

Answer 8

no not really.

Answer 9

but isnt it the same question?

Answer 10

w/ different numbers but they don't really explain it

Answer 11

I wonder if anyone else knows...

Answer 12

@uri help?

Answer 13

@AccessDenied help?

Answer 14

@nincompoop help?

Answer 15

@satellite73 help?

Answer 16

@hero help?

Answer 17

@radar help?

Answer 18

@precal help?

Answer 19

@agent0smith help?

Answer 20

@music101 does this help? http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Answer 21

I just want to check if my answer is right..

Answer 22

i got 906192???

Answer 23

i think thts correct isn't it?

Answer 24

I believe this is a combination question, because I don't think they care which of the 6 people sit in which seat. They just ask how many groups of 6 you can have

Answer 25

yea it is

Answer 26

Ok, so we'll evaluate 32 C 6, which as you said is equal to this:
\[\frac{ 32! }{ 6! \times (32-6)! }=\frac{ 32! }{ 6! \times 26! }\]

Answer 27

yup so im right

Answer 28

thanks

Answer 29

what abt this?

Answer 30

Ten elementary school students are eligible to be appointed to two positions: plant caretaker and chalkboard assistant. How many unique arrangements of these two positions are possible?

Answer 31

is it a permutation q.?

Answer 32

I don't remember the definition of permutation, but the answer will involve a factorial. (Or part of a factorial.)

Answer 33

@hero do i just do 10 P 2??

Answer 34

Just looked up permutation and the answer is yes, it is.

Answer 35

is this a combination question? & if so would u do 32 C 6 ?

correct.

Second one is a permutation because order matters, since the two positions are different.

Answer 36

yea so wouldn't i just do 10P2?

Answer 37

Yes.

Answer 38

because its a permutation question

Answer 39

ok so i got 90??

Answer 40

Or just 10*9.

There's 10 students for the first position, and 9 students left for the second.

Answer 41

ok thank u :)

Answer 42

when they say "how many UNIQUE arrangements are possible" can u say that its a permutation?? or..

Answer 43

Pretty much.

Arrangements = permutation. Arrangement means that order/position matters.

Answer 44

Groups = combination.

Answer 45

ok got it

Answer 46

Also, ways = permutation.

How many ways can ten people in a running race finish first/second/third = permutation question.

Answer 47

ok but i don't get this question:
Four people from a group of 300,000 radio listeners are eligible for a free vacation. How many different groups of vacationers are possible?

Answer 48

i did 300,000 C4 but its kinda complicated...

Answer 49

ill be back in a while but i still need help w/ this problem

Answer 50

Er yeah you'll get huge numbers with that one...

Answer 51

http://www.wolframalpha.com/input/?i=300%2C000+Choose+4

Answer 52

lol, my ipod calculator doesn't even do 300,000! which you need to actually calculate that. Just use the wolfram alpha result.

Answer 53

or simplify like so
\[\Large 300000 C 4 = \frac{ 300000! }{ 4! (300000- 4)!} = \]\[\Large \frac{ 300000! }{ 4! 299996! } = \frac{ 300000 *299999*299998*299997 }{ 4! }\]
and then your calculator can do it.

Answer 54

so then what would be the answer

Answer 55

I posted a link to it above.

Answer 56

... is that even the answer? or is that the wrong way to do it

Answer 57

Try calculating the one i gave above and see if you get the same answer.. this one
\[\Large \frac{ 300000 *299999*299998*299997 }{ 4! }\]

Answer 58

I got an answer with an E at the end of it

Answer 59

If you got something like 3.37 E20, that means\[ \large 3.37 \times 10 ^{20} \]

Answer 60

E at the end of a number on a calculator just means x10^

Answer 61

so I would put my answer in as 3.3749325*10^20???

Answer 62

what is:
a_______ is a grouping of k objects taken from a set of n elements?

Answer 63

is that a COMBINATION?

Answer 64

Well you can round it to 2 decimal places... 3.37*10^20.

There's a keyword in that question that tells you if it's a combination or permutation... remember these keywords from earlier: arrangements, groups, ways. Scroll back up if you forgot which is combination and permutation.

Answer 65

nvm I actually need help w/ this:

Answer 66

For your birthday, your parents take you to dinner and offer to let you have any 2 desserts on the menu. The restaurant, famous for its desserts, lists 10 on its menu. How many different combinations of 2 desserts can you order?

Answer 67

is it 10C2 or how do u do it

Answer 68

Well the C basically means choose. So how many desserts do you have to choose from? 10. And how many do you need to choose? 2.

Answer 69

oh ok then I got 45

Answer 70

but I don't know how he got 28...

Answer 71

nCr means "from n objects, choose r". Eg 10C2 = from 10 desserts, choose 2.

10C2 = 45.

Answer 72

ok and when a question says " how many unique itineraries are possible for u to choose", its a permutation right?

Answer 73

Yep, sounds like it. An itinerary is like a list, so order does matter.

Answer 74

ok

Answer 75

I got 151200

Answer 76

Well you didn't post the whole question so idk if that's right...

Answer 77

oh right :p

Answer 78

well there's 10 cities u want to go to but u only have time for 6

Answer 79

that's what the question basically says

Answer 80

so I used permutation and got that answer(151200)

Answer 81

Then 10P6 looks right, as does your answer.

Answer 82

i don't understand D:
i missed the "32 people tring to fit into several cars" question, the "10 elementary students appointed to 2 positions" question, the group of 7 musicians competing to earn 3 spots questions, and the one w/ the "E" answer question :( :(

Answer 83

i knew id probably miss that last one but not the others...

Answer 84

I'm not sure how you missed them, your answers here looked good.

At a family gathering, 32 people are trying to fit into several cars. Your car holds 6 people. How many different groups of 6 could you take in your car?

This should be 32C6, unless you're one of the 32 people and it's meant to be 31C6.

The 10 students should be 10P2.

the group of 7 musicians competing to earn 3 spots questions

^This is either 7C3 or 7P3, depending on the actual question.

And the one with the 'E' was 3.37*10^20.

Answer 85

i know D: I'll HAVE to talk to my teacher abt it. i missed 4 questions!!! that's horrible!

Answer 86

Well not really horrible, considering your answers appeared correct, based on the questions you posted here.

Answer 87

yea but the second time i took this its more like a mini-quiz and its like a B-minus...

Answer 88

my 1st one :( i cant repeat that grade though i don't like anything lower than an A

Answer 89

hey r u good @ conditional probability though

Answer 90

Well you can always check with the teacher, maybe the answer key was wrong. I'm pretty sure your answers were right.

Answer 91

its not an ans key though, u just submit an attachment and its like a computer scored assignment

Answer 92

I mean the computer scoring system might be off. I don't see how any of your answers were wrong.

Answer 93

yea ill ask my teacher abt it. so r u good @ conditional probablility

Answer 94

Yeah, probably.